Antenna requirements for software defined radio (SDR) and cognitive radio (CR) systems are reviewed and the resulting challenges are discussed. Both concepts imply capabilities for operation over very wide bandwidths, of the order of one decade in some cases. This then becomes the main challenge for antenna designers. However, as the concepts evolve, some systems will work over limited bandwidths and existing or extended bandwidth antennas will be used. In the Paper the concepts are explained. As bandwidth is a major concern, the fundamental limits of performance are restated. For handheld radio antenna bandwidth and efficiency at low frequencies is the main problem. Both in the terrestrial fixed infrastructure and in space communication the difficulty of designing very wideband arrays to give the pattern control necessary for interference minimization is significant. In defence applications external handset antennas are seen to be necessary and extension to very wide bandwidths is also seen to be challenging. It is concluded that there is steady progress towards the realization of both SDR and CR, and this is throwing up very significant antenna challenges.